March 13

Question 0

Find all the solutions of the equation
$x^2-9y^2=1$

Question 1

Find all the solutions of the equation
$x^2-5y^2=1$

Question 2

Find infinitely many solutions of the equation
$x^2-5y^2=11$
(there is no need to find all the solutions)

Question 3

Factor the Gaussian integer 5+15i into a product of non-unit Gaussian integers which can't be further factored as products of
non-unit Gaussian integers.